Question

A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.

Answer 1

0.102

Explanation:

The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)

Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.

The probability that exactly two modems in a random sample of five are defective is :

(10↓2)(70↓3) / (80↓5) = 0.102